Universal anomalous dimensions at large spin and large twist

TL;DR

This paper demonstrates the universality of anomalous dimensions of double trace operators at large spin and twist in conformal field theories across dimensions, using analytic bootstrap methods and holographic comparisons.

Contribution

It provides a universal analytic expression for anomalous dimensions at large spin and twist in arbitrary dimensions, validated by holographic calculations.

Findings

Anomalous dimensions are universal in the limit of large spin and twist.

Derived an approximate closed form for conformal blocks in any dimension.

Confirmed results through holographic duality comparisons.

Abstract

In this paper we consider anomalous dimensions of double trace operators at large spin ($\ell$) and large twist ($\tau$) in CFTs in arbitrary dimensions ($d\geq 3$). Using analytic conformal bootstrap methods, we show that the anomalous dimensions are universal in the limit $\ell\gg \tau\gg 1$. In the course of the derivation, we extract an approximate closed form expression for the conformal blocks arising in the four point function of identical scalars in any dimension. We compare our results with two different calculations in holography and find perfect agreement.